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/* Stable-sorting of an array using mergesort.
Copyright (C) 2009-2023 Free Software Foundation, Inc.
Written by Bruno Haible <bruno@clisp.org>, 2009.
This file is free software: you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as
published by the Free Software Foundation; either version 2.1 of the
License, or (at your option) any later version.
This file is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public License
along with this program. If not, see <https://www.gnu.org/licenses/>. */
/* This file implements stable sorting of an array, using the mergesort
algorithm.
Worst-case running time for an array of length N is O(N log N).
Unlike the mpsort module, the algorithm here attempts to minimize not
only the number of comparisons, but also the number of copying operations.
Before including this file, you need to define
ELEMENT The type of every array element.
COMPARE A two-argument macro that takes two 'const ELEMENT *'
pointers and returns a negative, zero, or positive 'int'
value if the element pointed to by the first argument is,
respectively, less, equal, or greater than the element
pointed to by the second argument.
STATIC The storage class of the functions being defined.
STATIC_FROMTO (Optional.) Overrides STATIC for the 'merge_sort_fromto'
function.
Before including this file, you also need to include:
#include <stddef.h>
*/
/* Merge the sorted arrays src1[0..n1-1] and src2[0..n2-1] into
dst[0..n1+n2-1]. In case of ambiguity, put the elements of src1
before the elements of src2.
n1 and n2 must be > 0.
The arrays src1 and src2 must not overlap the dst array, except that
src1 may be dst[n2..n1+n2-1], or src2 may be dst[n1..n1+n2-1]. */
static void
merge (const ELEMENT *src1, size_t n1,
const ELEMENT *src2, size_t n2,
ELEMENT *dst)
{
for (;;) /* while (n1 > 0 && n2 > 0) */
{
if (COMPARE (src1, src2) <= 0)
{
*dst++ = *src1++;
n1--;
if (n1 == 0)
break;
}
else
{
*dst++ = *src2++;
n2--;
if (n2 == 0)
break;
}
}
/* Here n1 == 0 || n2 == 0 but also n1 > 0 || n2 > 0. */
if (n1 > 0)
{
if (dst != src1)
do
{
*dst++ = *src1++;
n1--;
}
while (n1 > 0);
}
else /* n2 > 0 */
{
if (dst != src2)
do
{
*dst++ = *src2++;
n2--;
}
while (n2 > 0);
}
}
/* Sort src[0..n-1] into dst[0..n-1], using tmp[0..n/2-1] as temporary
(scratch) storage.
The arrays src, dst, tmp must not overlap. */
#ifdef STATIC_FROMTO
STATIC_FROMTO
#else
STATIC
#endif
void
merge_sort_fromto (const ELEMENT *src, ELEMENT *dst, size_t n, ELEMENT *tmp)
{
switch (n)
{
case 0:
return;
case 1:
/* Nothing to do. */
dst[0] = src[0];
return;
case 2:
/* Trivial case. */
if (COMPARE (&src[0], &src[1]) <= 0)
{
/* src[0] <= src[1] */
dst[0] = src[0];
dst[1] = src[1];
}
else
{
dst[0] = src[1];
dst[1] = src[0];
}
break;
case 3:
/* Simple case. */
if (COMPARE (&src[0], &src[1]) <= 0)
{
if (COMPARE (&src[1], &src[2]) <= 0)
{
/* src[0] <= src[1] <= src[2] */
dst[0] = src[0];
dst[1] = src[1];
dst[2] = src[2];
}
else if (COMPARE (&src[0], &src[2]) <= 0)
{
/* src[0] <= src[2] < src[1] */
dst[0] = src[0];
dst[1] = src[2];
dst[2] = src[1];
}
else
{
/* src[2] < src[0] <= src[1] */
dst[0] = src[2];
dst[1] = src[0];
dst[2] = src[1];
}
}
else
{
if (COMPARE (&src[0], &src[2]) <= 0)
{
/* src[1] < src[0] <= src[2] */
dst[0] = src[1];
dst[1] = src[0];
dst[2] = src[2];
}
else if (COMPARE (&src[1], &src[2]) <= 0)
{
/* src[1] <= src[2] < src[0] */
dst[0] = src[1];
dst[1] = src[2];
dst[2] = src[0];
}
else
{
/* src[2] < src[1] < src[0] */
dst[0] = src[2];
dst[1] = src[1];
dst[2] = src[0];
}
}
break;
default:
{
size_t n1 = n / 2;
size_t n2 = (n + 1) / 2;
/* Note: n1 + n2 = n, n1 <= n2. */
/* Sort src[n1..n-1] into dst[n1..n-1], scratching tmp[0..n2/2-1]. */
merge_sort_fromto (src + n1, dst + n1, n2, tmp);
/* Sort src[0..n1-1] into tmp[0..n1-1], scratching dst[0..n1-1]. */
merge_sort_fromto (src, tmp, n1, dst);
/* Merge the two half results. */
merge (tmp, n1, dst + n1, n2, dst);
}
break;
}
}
/* Sort src[0..n-1], using tmp[0..n-1] as temporary (scratch) storage.
The arrays src, tmp must not overlap. */
STATIC void
merge_sort_inplace (ELEMENT *src, size_t n, ELEMENT *tmp)
{
switch (n)
{
case 0:
case 1:
/* Nothing to do. */
return;
case 2:
/* Trivial case. */
if (COMPARE (&src[0], &src[1]) <= 0)
{
/* src[0] <= src[1] */
}
else
{
ELEMENT t = src[0];
src[0] = src[1];
src[1] = t;
}
break;
case 3:
/* Simple case. */
if (COMPARE (&src[0], &src[1]) <= 0)
{
if (COMPARE (&src[1], &src[2]) <= 0)
{
/* src[0] <= src[1] <= src[2] */
}
else if (COMPARE (&src[0], &src[2]) <= 0)
{
/* src[0] <= src[2] < src[1] */
ELEMENT t = src[1];
src[1] = src[2];
src[2] = t;
}
else
{
/* src[2] < src[0] <= src[1] */
ELEMENT t = src[0];
src[0] = src[2];
src[2] = src[1];
src[1] = t;
}
}
else
{
if (COMPARE (&src[0], &src[2]) <= 0)
{
/* src[1] < src[0] <= src[2] */
ELEMENT t = src[0];
src[0] = src[1];
src[1] = t;
}
else if (COMPARE (&src[1], &src[2]) <= 0)
{
/* src[1] <= src[2] < src[0] */
ELEMENT t = src[0];
src[0] = src[1];
src[1] = src[2];
src[2] = t;
}
else
{
/* src[2] < src[1] < src[0] */
ELEMENT t = src[0];
src[0] = src[2];
src[2] = t;
}
}
break;
default:
{
size_t n1 = n / 2;
size_t n2 = (n + 1) / 2;
/* Note: n1 + n2 = n, n1 <= n2. */
/* Sort src[n1..n-1], scratching tmp[0..n2-1]. */
merge_sort_inplace (src + n1, n2, tmp);
/* Sort src[0..n1-1] into tmp[0..n1-1], scratching tmp[n1..2*n1-1]. */
merge_sort_fromto (src, tmp, n1, tmp + n1);
/* Merge the two half results. */
merge (tmp, n1, src + n1, n2, src);
}
break;
}
}
#undef ELEMENT
#undef COMPARE
#undef STATIC
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